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Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces

Received: 30 May 2015    Accepted: 1 June 2015    Published: 15 June 2015
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Abstract

In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.

Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1)

This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015)

DOI 10.11648/j.ajam.s.2015030301.17
Page(s) 41-45
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Multivalued Mapping, Upper and Lower Semicontinuous, t-norm, Fuzzy Metric Space

References
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[3] J.P. Aubin, J. Siegel, Fixed point and stationary points of dissipative multivalued maps, Proc. Amer. Math. Soc. 78, 391–398 (1980).
[4] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29, 531–536 (2002).
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[8] Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings. J. Math. Anal. Appl. 317, 103-112 (2006)
[9] A. George, P. Veeramani, On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395-399 (1994).
[10] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365-368 (1997).
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[14] F. Kiany, A. Amini-Harandi, Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces. Fixed Point Theory Appl. doi:10.1186/1687-1812-2011-94 (2011).
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[18] D. Mihe , On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets Syst. 158, 915-921 (2007).
[19] S. B. Nadler Jr., Multivalued contraction mappings, Pacific Journal of Mathematics 30, 475–488 (1969).
[20] A. Razani, A contraction theorem in fuzzy metric space. Fixed Point Theory Appl. 2005(3), 257-265 (2005).
[21] J. Rodrguez-López, S. Romaguera, The Hausdorff fuzzy metric on compact sets. Fuzzy Sets Syst. 147, 273-283 (2004).
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[23] T. Som, R. N. Mukherjee, Some fixed point theorems for fuzzy mappings. Fuzzy Sets Syst. 33, 213-219 (1989).
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Cite This Article
  • APA Style

    Basit Ali, Mujahid Abbas. (2015). Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. American Journal of Applied Mathematics, 3(3-1), 41-45. https://doi.org/10.11648/j.ajam.s.2015030301.17

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    ACS Style

    Basit Ali; Mujahid Abbas. Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. Am. J. Appl. Math. 2015, 3(3-1), 41-45. doi: 10.11648/j.ajam.s.2015030301.17

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    AMA Style

    Basit Ali, Mujahid Abbas. Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. Am J Appl Math. 2015;3(3-1):41-45. doi: 10.11648/j.ajam.s.2015030301.17

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  • @article{10.11648/j.ajam.s.2015030301.17,
      author = {Basit Ali and Mujahid Abbas},
      title = {Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {3-1},
      pages = {41-45},
      doi = {10.11648/j.ajam.s.2015030301.17},
      url = {https://doi.org/10.11648/j.ajam.s.2015030301.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.17},
      abstract = {In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.},
     year = {2015}
    }
    

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    AU  - Mujahid Abbas
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    DO  - 10.11648/j.ajam.s.2015030301.17
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    AB  - In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.
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Author Information
  • Department of Mathematics, University of Management and Technology, Johar Town Lahore, Pakistan

  • Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

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